Data-Driven Robust Control for Type 1 Diabetes 215The concept of closed-loop control of insulin, a.k.a. the artificial pancreas
(AP), involves a continuous glucose monitor (CGM) that provides glucose mea-
surements (with a typical period of 5 min) to a control algorithm running inside
the insulin pump or on a peripheral device (e.g. smartphone or tablet) connected
to the pump [ 38 ]. The controller adjusts the insulin therapy to maintain healthy
BG levels and to avoidhyperglycemia(BG above the healthy range) as well as
hypoglycemia(BG below the healthy range). AP systems have been extensively
studied in the last 20 years [ 10 ], but only lately cleared for clinical trials [ 17 , 22 ]
and commercialization.
The recently FDA-approved MINIMED 670G by Medtronic^1 is the first com-
mercial AP system, and can regulate the basal insulin rate automatically. It
is referred to as a “hybrid closed-loop” device as patients need to manually
announce the amount of carbohydrate (CHO) and time of each meal to receive
the appropriate bolus insulin dose. This manual procedure is a burden to the
patient and inherently dangerous as incorrect information can lead to incorrect
insulin dosage and, in turn, harmful BG levels.
While meals are the major source of uncertainty in BG control, another
important factor is physical activity, which accelerates glucose absorption and
thus requires a reduced insulin dosage. To build fully automatedclosed-loopAP
systems, it is essential to design insulin control algorithms that arerobustto the
patient’s behavior and activities.
In this paper, we propose adata-driven, robust model-predictive control
(robust MPC) framework for the closed-loop control of insulin administration,
both basal and bolus, for T1D patients under uncertain meal and exercise events.
Such a framework seeks to eliminate the need for meal announcements by the
patient, to fully automate insulin regulation. We capture the wide range of indi-
vidual meal and exercise patterns usinguncertainty setslearned from historical
data.
Following [ 1 ], we construct uncertainty sets from data so that they cover
the underlying (unknown) distribution with prescribed probabilistic guaran-
tees. Leveraging such information, our robust MPC system computes the insulin
administration profile that minimizes the worst-case performance with respect
to these uncertainty sets, so providing a principled way to deal with uncertainty.
Besides uncertainty, another challenging aspect of closed-loop control isstate
estimation, which is needed to recover the full state of the model (used within
MPC) from CGM measurements. Not only are these measurements noisy and
delayed with respect to BG (the CGM detects glucose in the interstitial fluid),
but we also need to estimate, along with the state, current meal and exercise
uncertainties.
For this purpose, we designed a moving-horizon state estimator (MHE) [ 6 , 20 ,
27 ] that, similar to MPC, exploits a prediction model to find the most likely state
estimate given the observations. Crucially, data-driven uncertainty sets improve
the estimation by constraining the admissible meal and exercise uncertainties.
(^1) https://www.medtronicdiabetes.com/products/minimed-670g-insulin-pump-
system.